2023 S1-05 Mathematics: 2. Real Numbers

1. Equal, Less than or Greater than sign

> Greater than

5 > -12
n > 20 where n is a prime number.

Then n = 23, 29, 31, 37, 41, etc...

≥ Greater than or equal

n ≥ -1 where n is an integer. It means include -1 if it satisfies the given condition

Then n = -1 (i.e. including the number), 0, 1, 2, 3, 4....

< Less than

20 < 23
n < 20 where n is a natural number

Then n = 1, 4, 9, 16

≤ Less than or equal

n ≤ 25 where n is a multiple of 3. It means include 25 if it satisfies teh given condition.

Then n = 24, 21, 18, 15, 12, 9, 3, 0, -3, -6, ...

Watch the following clip for a Preview of what we will be doing in the next few lessons.

2. Number Lines

3. Real Numbers

4. Operations of Numbers

Integers - Zero Pairs (Basic Concept)

The sum of an integer and its opposite is ZERO

E.g. 1: - 20 + 20 = 0
E.g. 2: 56 + (-56) = 0
E.g. 3: -28 + 28 = 0

Integers - Addition of Integers (Basic Concepts)

Evaluate - 3 + (-2)

Rule: To add two negative numbers, add their absolute values and take the negative sign for the answer

E.g. 1: -25 + (-17) = -42
E.g. 2: -21 + (-21) = -42
E.g. 3: -18 + (-11) = -29

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Evaluate 3 + (-7)

Rule: To add 2 integers of different signs such that the negative integer has a larger absolute value, we find the difference between their absolute value and take the negative sign for the answer.

E.g. 1: -17 + 12 = -5
E.g. 2: 52 + (-67) = -15
E.g. 3: -88 + 85 = -3
E.g. 4: 28 + (-82) = -54

Rule: To add 2 integers of different signs such that the positive integer has a larger absolute value, we find the difference between their absolute value and take the positive sign for the answer.

E.g. 1: -12 + 17 = 5
E.g. 2: -63 + 68 = 5
E.g. 3: 86 + (-53) = 33
E.g. 4: -38 + 83 = 45

Integers - Subtraction (Basic Concepts)

Evaluate - 2 - 6
Note: Zero Pairs are introduced.

Evaluate - 5 - (-3)

Evaluate 5 - (-7)
Note: Zero Pairs are introduced.

Multiplication (Basic Concepts)

Draw comparison between 2 x 3 (i.e. 2 groups of positive 3)
and 2 x (-3) (i.e. 2 groups of negative 3)

2 x 3 = 6
2 x (-3) = -6

Division (Basic Concepts)

Draw comparison between 8 ÷ 2

and (-8) ÷ 2

8 ÷ 2 = 4

(-8) ÷ 2 = -4

Using Number Line to Explain...
(A) Adding and Subtracting Negative Numbers

(B) Adding Negative Numbers:
Find: -45 + (-46) + (-29)

(C) Adding Integers of Different Signs
Find: 15 + (-46) + 29

(D) Multiplying 2 Negative Numbers

NOTE 1: We will need to recall how distributive law works

e.g. 2 x 7 = 2 x (3 + 4)

which can be written as = (2 x 3) + (2 x 4)

Note 2: We will need to recall the property of ZERO Pair

e.g. 4 + (-4) = 0

e.g. (-3) + 3 = 0